Textbook: The recorded lectures together with the posted lecture slides will provide a self-contained coverage of the material. The role of the textbooks is to provide additional examples and in-depth coverage of the topics, as well as homework problems and optional material that we will not have time to cover in class.
Douglas E. Ensley and J .Winston Crawley, ‘Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games Wiley Press, 2005. It’s pretty expensive (especially the hardcover version), but there are cheaper options of renting it or buying it used, e.g., on eCampus or here. Do not buy the paperback “solutions manual” in place of the main textbook. The textbook contains links to (free!) online practice activities that can augment the lectures and assignments. The activities can be found here. (Note that you may need to enable Macromedia Flash in your browser.)
As an additional source of explanations and practice problems, I recommend the following open source texts:
Course Prerequisites: The material of the course does not overlap much with that of the conventional pre-calculus and calculus courses, but it will demand some basic skill in calculation and algebra. There is no formal prerequisite, but an average high-school math background will be useful, e.g., the University’s R1 gen-ed requirement. (This course does not carry gen-ed credit itself.)
Lectures are asynchronous and will be posted week by week, along with the lecture slides. There will in general be two 1-hour lectures per week, each divided into roughly three 20-minute segments. After watching all of the segments of a lecture, take the brief quiz on the lecture. The quiz should be pretty straightforward if you have watched the lecture. In general, Lectures will be made available Monday (quiz due by Tuesday 11:59pm Amherst time) and Wednesday (quiz due by Thursday 11:59pm Amherst time). Slides for the week’s lectures will be posted on Friday. If you are experiencing technical difficulties, UMass IT technical support can be found at UMass IT support.
Grading and evaluation:
Midterm exams (35%): There will be three non-cumulative exams whose goal is to help you synthesize what you have learned. The one with the highest grade with count for 15% of the course grade, and the other two each will count for 10% of the final grade. for You will have up to two hours for an exam that we hope will be doable in one hour. We will make up a practice exam, similar in length and difficulty to the real exam, and post it a week before the real exam. We’ll then post solutions to the practice exam with a few days to go. The last exam will take place during the final exam period.
Homework (35%): These will usually be assigned on Friday, and due the following Friday by 11:59pm Amherst Time. We will drop your worst homework when computing your course grade.
Quizzes (30%): A quiz will be posted right after the class slot due the following day by 11:59pm Amherst time. These are very short quizzes (~15-30 minutes) to make sure that you are following the material.
Class participation (10%): Up to 10% extra credit may be awarded for class participation. This may come in many forms, e.g., active participation in Piazza discussions and office hours, and asking good clarifying questions and answering other students’ or instructor questions on Piazza.
Late submission policy: It is essential that the homework is completed on or before the deadline. No work will be accepted after the deadline unless you have a valid medical reason that is approved by the instructor before the deadline.
Disability Services: UMass Amherst is committed to making reasonable, effective, and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a documented disability on file with Disability Services, you may be eligible for reasonable accommodations in this course. If your disability requires accommodation, please notify me within the first two weeks of the course so that we may make arrangements in a timely manner.
This is the home page for INFO 150, an introductory undergraduate course in discrete mathematics and the mathematical method. It has been developed for use in the Informatics degree program in the College of Information and Computer Sciences, which focuses on the application of computational principles and techniques to advance other disciplines. The intended audience for this course comprises students who intend to pursue computing, perhaps in programming courses for majors like CMPSCI 121 and 187, but could use more exposure to mathematical thinking first.
Schedule and Topics
Course Overview; Number Puzzles and Sequences
Kwong Sec 1.3 and 1.4; E&C Sec 1.2
Truth-tellers, Liars, and Propositional Logic; Predicates
E&C Sec 1.3 & 1.4
Fri Feb 12 is the end of Add/Drop
Implications; Brute-Force Search
E&C Sec 1.4 & 1.5; Notes
Mathematical Writing and Proofs
E&C Sec 2.1 & 2.2; Notes
E&C Sec 2.3 & 2.4
Proving Program Correctness
Exam 1 on Friday
E&C 3.1–3.3; Kwong Ch 4
Functions and Relations
E&C 4.1–4.3; Kwong Ch 6 & Ch 7
Combinatorics: Basic Rules for Counting
E&C Sec 5.1-5.4; Kwong Ch 8; Levin Ch 1
Combinatorics: Arithmetic Triangle
E&C Sec 5.3;
Exam 2 on Friday
E&C Sec 6.1-6.4
E&C Sec 7.1-7.2
Exam 3 on May 1 (tentative)
Discussion and Grading
We will use Piazza for discussions and posting lecture notes. We will use piazza for communication and interaction outside of class hours. We will sign you up using your email address on SPIRE. Please let us know immediately if you are unable to access piazza or if you need another email address included. We will use Piazza for discussions and other interactions outside of class hours. On Piazza, you can ask questions about the course material, discuss solutions to problems, etc. You can even ask questions anonymously if you wish to do so. Please make sure you monitor piazza regularly throughout the semester.
We will be using Gradescope for grading homeworks and exams. You will need to set up a Gradescope account if you don’t have one. Then you will need to enroll in INFO 150 using an access code that is provided in Piazza. When turning in assignments, you will need to upload them to Gradescope as images or as a pdf file; ask one of the teaching team or go to the Gradescope help page. Please make sure to label all problems clearly, and use a separate page for each problem. Assignments must generally be submitted by 11:59pm on the day that they are due. See the “Course Information” tab for policies on late homeworks.